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| − | If a linear system has a response to <math> | + | If a linear system has a response to <math>e^(2jt)</math> of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t). |
Revision as of 06:57, 15 September 2008
Linearity
If a linear system has a response to $ e^(2jt) $ of t*exp(-2jt) and a response to exp(-2jt) of t*exp(2jt), then it's response to cos(2t) must be t*cos(-2t).
Explanation:
The system seems to have the following characteristics:
x(t) --> SYSTEM --> t*y(-t)
Therefore, if we put the change the input from x(t) (above) to cos(2t), then it should output the signal t*cos(-2t).
